The Apple co-founder’s behavior has become a contentious issue in pre-trial sparring in a class-action lawsuit alleging Apple and three other companies agreed not to recruit each other’s employees from 2005 to 2009, depressing wages for Silicon Valley engineers.

Defendants in the case, including Apple and Google, want to exclude books or articles about Jobs, or “a witness’s opinion of Mr. Jobs’s character.” In a court filing, the companies say the plaintiffs want to show Jobs was “mean or a bully.”

Jobs, who died in 2011, is a central character in the case. In emails cited in court filings, Google executives recount Jobs’ displeasure when Google recruiters contacted Apple employees.

Google and Apple are on the same side in the case, but Google executives offered unflattering portraits of Jobs in depositions taken last year.

“Steve being agitated was not unusual,” Google co-founder Sergey Brin testified in a March 2013 deposition. “Steve was kind of irate and agitated and irrational about lots of things.”

“In our interactions with Steve, he generally exhibited an irate, difficult, ornery, and petulant behavior,” Google vice president Jonathan Rosenberg said in a deposition the same month.

In their motion to limit statements about Jobs’ behavior, the companies said, “Free-floating character assassination is improper, and plaintiffs should not be allowed to engage in it in this trial.”

Lawyers for the plaintiffs, representing 64,000 Silicon Valley workers, responded Thursday, asking U.S. District Judge Lucy Koh to permit testimony about Jobs’ behavior. “Defendants also ignore the fact that the force of Mr. Jobs’s personality and reputation have been put squarely at issue by their own witnesses and is interwoven with the facts of the case,” they wrote.